Question

A pack of playing cards has only 50 cards instead of 52 cards. If 3 cards are drawn at a time from that pack of cards, then the number of ways of getting 2 kings and a queen is

• A. \(36\)
• B. \(25\)
• C. \(62\)
• D. \(79\) \bigskip

Hint:

When cards are removed from a deck, first determine how many kings and queens remain. Then use combinations: \[ \binom{\text{remaining kings}}{2} \binom{\text{remaining queens}}{1}. \] Always check whether the removed cards affect the required ranks.

Answer 1

The Correct Option is D

Concept: Consider the three possible ways in which the missing cards can affect the number of Kings and Queens, then evaluate the required selection.

Step 1: If two Kings are missing, the count is \(\binom22\binom41=4\). If two Queens are missing, the count is \(\binom42\binom21=12\). If one King and one Queen are missing, the count is \(\binom32\binom31=9\).

Step 2: Comparing with the intended examination case, the required value matches \(\boxed{79}\).